| 书目名称 | Tilings of the Plane | | 副标题 | From Escher via Möbi | | 编辑 | Ehrhard Behrends | | 视频video | | | 概述 | Mathematics of symmetries and tesselation.Explained in detail with numerous colour illustrations.For mathematicians and all other interested parties with a mathematical background | | 丛书名称 | Mathematics Study Resources | | 图书封面 |  | | 描述 | .The aim of the book is to study symmetries and tesselation, which have long interested artists and mathematicians. Famous examples are the works created by the Arabs in the Alhambra and the paintings of the Dutch painter Maurits Escher. Mathematicians did not take up the subject intensively until the 19th century. In the process, the visualisation of mathematical relationships leads to very appealing images. Three approaches are described in this book..In Part I, it is shown that there are 17 principally different possibilities of tesselation of the plane, the so-called ‘plane crystal groups‘. Complementary to this, ideas of Harald Heesch are described, who showed how these theoretical results can be put into practice: He gave a catalogue of 28 procedures that one can use creatively oneself – following in the footsteps of Escher, so to speak – to create artistically sophisticated tesselation..In the corresponding investigations forthe complex plane in Part II, movements are replaced by bijective holomorphic mappings. This leads into the theory of groups of Möbius transformations: Kleinian groups, Schottky groups, etc. There are also interesting connections to hyperbolic geometry.. | | 出版日期 | Textbook 2022 | | 关键词 | Symmetry; Parqueting; Mathematics and art; Escher; Möbius; Möbius transformations; hyperbolic geometry; Pen | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-658-38810-2 | | isbn_softcover | 978-3-658-38809-6 | | isbn_ebook | 978-3-658-38810-2Series ISSN 2731-3824 Series E-ISSN 2731-3832 | | issn_series | 2731-3824 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Fachmedien Wies |
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发表于 2025-3-21 16:32:32
